Photos/videos are not allowed in the Amory in the Kremlin. I was in there today, and they told me "nelzya".
Some places photos are permitted if you pay extra. I was in Moscow in 2011, and two places where this was the case was the Space Museum by VDNKh metro station, and the Red Army Museum by Dostoyevskaya metro station.
I had no issues shooting video or photos in the State Historical Museum, Patriotic War of 1812 Museum, St. Basil's Cathedral, Great Patriotic War Museum, Ostankino Tower, Retro Cars Museum, Pushkin Museum.
In St. Petersburg, the only place where photos/videos are nelzya (to which I've visited) was Peterhof.